Does it matter if there is some floating debris after centrifuging your ammonium sulfate cuts? You can just scoop it out carefully and then pour off supernatant, leaving behind your pellet. Wash pellet once with the same ammonium sulfate concentration and re-spin to be sure you get rid of it all.
Alternatively, is it absolutely necessary to have Triton in your lysis buffer? This is probably why you have lipids in your ammonium sulfate pptn's. Try lysing your cells without triton (sonication or french press), then spin down the membranes by centrifugation at >40k x g for 1 hr. Remove the soluble fraction (supernatant) and then do your ammonium sulfate cuts as you did before. If that fluffy stuff really is lipids, then it shouldn't be there doing it this way.
I didn't read that protocol, but when doing ammonium sulfate cuts it's best to add the ammonium sulfate over the course of 30 min while stirring. I usually add 1/3 of the AS at time 0, 1/3 at 15 min, and 1/3 at 30 min...stir for at least an hour (up to overnight), then pellet. All of this of course is done at 4C in my experience.